Problem 7 · 2013 Math Kangaroo
Easy
Spatial & Visual Reasoning
cube-viewscareful-counting
Nathalie wanted to build a large cube out of lots of small cubes, just like in Picture 1. How many cubes are missing from Picture 2 that would be needed to build the large cube?
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Answer: C — 7
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Hint 1 of 3
A full big cube like Picture 1 is 3 cubes wide, 3 deep and 3 tall, so it needs 27 small cubes.
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Hint 2 of 3
Count how many small cubes are really in Picture 2, layer by layer.
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Hint 3 of 3
The missing number is 27 take away the cubes you counted in Picture 2.
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Approach: subtract the cubes present from a full cube
- A complete large cube is 3 × 3 × 3 = 27 small cubes.
- Counting the cubes in picture 2 layer by layer gives 20 cubes.
- So 27 − 20 = 7 cubes are missing.
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